covariant

Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

adj. Physics Expressing, exhibiting, or relating to covariant theory.

adj. Statistics Varying with another variable quantity in a manner that leaves a specified relationship unchanged.

from Wiktionary, Creative Commons Attribution/Share-Alike License

adj. (Of a functor) which preserves composition

adj. Using or relating to covariance.

from the GNU version of the Collaborative International Dictionary of English

n. A function involving the coefficients and the variables of a quantic, and such that when the quantic is lineally transformed the same function of the new variables and coefficients shall be equal to the old function multiplied by a factor. An invariant is a like function involving only the coefficients of the quantic.

from The Century Dictionary and Cyclopedia

n. In mathematics, a function which stands in the same relation to the primitive function from which it is derived as any of its linear transforms to a similarly derived transform of its primitive; a function of the coefficients and variables of a given quantic, such that when the quantic is linearly transformed, the same function of the new variables and coefficients is equal to the old function multiplied by some power of the modulus of transformation. Covariants were discovered by Cayley, and so named by Sylvester, 1852.

adj. changing so that interrelations with another variable quantity or set of quantities remain unchanged

Etymologies

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Examples

Over the previous year, he had been determined to find a gravitation theory that was generally covariant, that is, whose equations were unchanged by arbitrary transformation of the spacetime coordinates.

The main problem for the latter is the general covariance of the field equations of General Relativity: any spacetime model and its image under a diffeomorphism (a infinitely differentiable, one-one and onto mapping of the model to itself) are in all observable respects equivalent to one another; all physical properties are expressed in terms of generally covariant relationships between geometrical objects.

Being that the supersymmetry variation of the gravitino is the covariant derivative of the local spinor parameterizing the supersymmetry transformation, this would seem to always imply that the condition for supersymmetry is that there must exist a covariantly constant spinor field.